結合影像暨感測器資訊之三維模型重建研究

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(1)Based on the information of image and IMU sensor for 3D reconstruction. 106. 8.

(2)

(3) (3D Reconstruction).

(4) ABSTRACT 3D reconstruction is the process of capturing the shape and appearance of real objects from the keyframe of different viewpoint. Through the projection of two-dimensional materials to restore three-dimensional space, which is similar to a binocular vision for the position. Nowadays, a 3D model is implemented in many applications, from an image reverts into a stereoscopic model as the original real object, that can be given more details of texture and structure. First, based on the mobile device to scan around the object for video recording, using structure from motion(SfM) algorithm to calculate the relationship of camera position and scene geometric. Meanwhile, at the scanning stage, the sensor data are acquired along with tracks of features in the video. All these data are used to build a camera trajectory using above image techniques after scanning is completed. According to information support of sensor geography with robustness and stability, which can be demonstrated the second validation on positioning, not only enhance the accuracy of the 3D model, but also improve the efficiency. Keyword: 3D Reconstruction, Sensor, Structure from Motion, Affine-SIFT.

(5) Python. Galileo. Intel. Intel Joseph. Thanks be to God..

(6) III IV 1 1.1. ………………………………………………….……………1. 1.2. ………………………………………………………….……2. 1.3. ……………………………….………………………3. 1.4. ……………………………….…………………………3 5. 2.1. ……………………………….…………………………5. 2.2. ………………………………………………….7 2.2.1. ………………………………………………………8. 2.2.2. ………………………………………………..12. 2.2.3. …………………………………………………..17 22. 3.1. ………………………………………….……………………22. 3.2. (KeyFrame Extraction) ……………………………….25. 3.3. (Structure from Motion, SfM) ……………………..27 3.3.1. …………………………………….………………...29. 3.4. (IMU sensor Information) 3.4.1. 30. ……………………………………………………..30. 3.4.2 GPS. …………………………………………………34. 3.4.3 7-DoF. (Similarity Transform) …………………..….37 42. 4.1. ……………………………………………………………...42. 4.2. 43 4.2.1. …………………….………………...43. 4.2.2. ………………………………53 I.

(7) 4.2.3. …………………………….56 59. 5.1. ………………………………………………………………59. A. 60. B. 68 …………………….…………………………………….……………79. II.

(8) 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 A.1 A.2 A.3 A.4 A.5 A.6 B.1 B.2 B.3 B.4 B.5 B.6 B.7. …………………………………………………………………9 ………………………………………………………………..10 ASIFT …………………………………………………..12 ………………………………………………………..13 ……………………………………………………………………..15 ……………………………………………………..19 EXIF ………………………………………………………………19 GPS ……………………………………………..20 GPS ………………………………………………………..21 …………………………………………………………………..22 360 ………………………………………………………..23 ……………………………………………………23 (SfM) ………………………………………………24 ………………………………………………..24 …………………………………………………..25 ……………………………………..26 (SfM) ………………………………………………28 (Geocentric Longitude) (Geocentric Latitude) ..31 ………………………………………………………………32 ……………………………………………………………33 ……………………………………………………38 SfM GPS …………………………………………39 ………………………………………………40 …………………………………………41 SIFT ……………………………………………………………60 ……………………………………………………….63 ………………………………………………….64 ……………………………………….65 SIFT ………………………………………………66 SIFT ………………………………………………………………67 ……………………………………………………………….69 ……………………………………………………………….70 ……………………………………………………………….71 ……………………………………………………….72 ……………………………………………………….73 ……………………………………………………….74 ……………………………………………………….76. III.

(9) 1– 2– 3– 4– 5– B.1 –. …………………………………………………………42 ……………………………………………………………42 …………………………………………………………43 ……………………………………………………………………51 ……………………………………………………………………56 …………………………………………………74. IV.

(10) . 1.1. 3D Reconstruction. 1 2. 3 4. 1.

(11) . 1.2 3D. 3D Printing. 3D. 3D. 3D. 3D. 3D. 2. *.stl.

(12) . 1.3. 180. 1.. 2.. 3.. 1.4. 3.

(13) . 4.

(14) . 2.1 2.2. 2.1 (3D model) (Grid). (Texture) (XYZ). (Intensity). (RGB ). [1] Autodesk 123D Catch [2]. 2D 3D. (. ). /. (Autodesk, Inc.). 5. 3D.

(15) . (Photogrammetry). VisualSFM (A. Visual Structure from Motion System) [3]. SIFT. Changchang Wu. [4]. RANSAC (SFM). [5]. [6]. 3D Meshlab[7] VisualSFM 3D. Furukawa 2007 Stereo Software) [8] [9]. 2010. 2D. PMVS (Patch-based Multi-view. CMVS (Clustering Views for Multi-view Stereo). SfM. Bundler. 6.

(16) . PMVS Bundler. CMVS. PMVS. 2.2. 2.2.1. — (ASIFT). 2.2.2. — 2.2.3. [10][11]. 7. —. SIFT.

(17) . (GPS) (Accelerometer). (magnetometer). (Gyroscope). [12][13]. Google project. Tango [12]. (. ). Tanskanen [13]. 2.2.1 —. 8.

(18) . 2.1. ( (Gray-Level). ) [14]. 9.

(19) . §. (Feature Point) (1). (Detection) (2). (Description). (Matching) point). (Interesting (robustness). (Edge). (1). (Flat):. (3). (Corner). 2.2. 2.2. (3). 10. (2).

(20) . (Descriptor). (Scale-Invariant Feature Transform, SIFT) 2004. David Lowe 1999. [4] A (ASIFT). SIFT J.M. Morel G.Yu 2009. (ASIFT) [15]. SIFT (Longitude angle;. ). (Latitude angle;. ). ASIFT SIFT. 2.3. B. 11.

(21) . 2.3. ASIFT. [15]. 2.2.2. (intrinsic parameters) (extrinsic parameters) 8 (focal length) (image center). (pixel size). (radial distortion coefficient) (translation vector) (rotation matrix). 12.

(22) . 2.4. (", $, %) (. ("' , $' , %' ). 2.1). -. += 0 0. / -2 0. (0 788 *0 ; 6 = 798 7:8 1. "' () $ / *) = + ' = +6 %' 1 1. X Y % 1. ((0 , *0 ). 789 799 7:9. 7:8 7:9 7::. (. 2.3). (. +. (() , *) ). CCD. 13. ;8 ;9 ;:. ). +. (. 2.1). (. 2.2).

(23) . ;:×8. ?:×:. ( (. 3×4. 2.2). 6. 2.3). §. (Epipolar Geometry). (Fundamental Matrix) 2.5. +. BC. BD. (Epipolar Plan). BC ℯC. ℯD. (epipole). 14. BD. (baseline).

(24) . 2.5 L R +C = "C , $C , %C. BC +D = ["D , $D , %D ]. KC = (C , *, LC (. HC. HD. ". KD = [(D , *D , LD ]. (C. (D. 2.4). (C = HC L (C. BD. MN ON. ; (D = HD +. (D. MP OP. BC. (. 2.4). (C. R. (D. R (epipolar. constraint). 15.

(25) . 3×3 Q BC. ?. +C. 6 = BD −. +D. +C = + − BC = ["C , $C , %C ]S ; +D = + − BD = ["D , $D , %D ]S ® +D = ?(+C − 6). (. 2.5). (+C − 6)S 6 ×+C = 0. (. 2.6). (?S +C )S 6 ×+C = 0. (. 2.7). 9. 6×+C = T+C. 0 T = 6U −62. −6U 0 6.. 62 −6. 0. +DS V+C = 0 V = ?T. (. (. 2.8). 2.9). (Essential matrix) +C. 2.9. (. 2.10. +D. WC. +C = WC X8 KC ; +D = WD X8 KD. ). Q = WD XS VWC X8. 16. [16]. WD.

(26) . KDS QKC = 0. (. 2.10) YC. 2.5. YD = QKC ; YC = Q S KD KC. (. KD Q. ZDS Q = 0 ; QZC = 0. 2.11). 2.10. (. 2.12). 2.2.3 (Sensor) GPS. [17]. 17. YD.

(27) . (data rate). [18]. Metadata( IIM XMP. ) EXIF. 2.6 IPTC. 1994. IIM(Information Interchange Model) XML Adobe. 2001. XMP. IPTC IIM. XML. utf8. EXIF Exchangeable image file format 1996. GPS ……. 2.7. 18.

(28) . 2.6. 2.7. EXIF. (. [. 1]). (Global Positioning System GPS). 2.8. 19.

(29) . 2.8. GPS. [22]. GPS. GPS. 24. GPS. GPS (Assisted Global Positioning. System AGPS). GPS (. 2.9). AGPS. [19]. 20.

(30) . WiFi. WiFi (. ). [20] GPS [21] 95. 0.715 4.9. (16. ). GPS. (2.3. ) [22]. GPS. (centimeter). (millimeter). 2.9. GPS. [21]. 21. GPS.

(31) . 3.1. 3.2. 3.3 (Structure From Motion, SfM) (1). (2). a. 3.4. GPS. 3.1 3.1. 3.1. 22. b. IMU information.

(32) . 1.3. 180 3.2. 3.2. 360. 3.3. 3.3. 23.

(33) . SfM. (Meshlab) [7]. 3.4. 3.4. (SfM). 3.5. 24.

(34) . 3.2 (Key Frame). 3.6. 3.6. 25.

(35) . (Frame) (Frame Per Second; FPS) 24(. / ) 0.5 60. 3.7. SIFT. 3.7. 26. 6. 6/6.

(36) . 3.3. (Structure From Motion, SfM). 1. (DfM: Depth from Motion). 2. (SfM: Structure from Motion). 3. (Dff: Depth from focus, Linear perspective). 4. (1). (2). (Structure from Motion, SfM)[6]. 27.

(37) . SfM. 3.8. (bundle adjustment) [23]. 3.8. (SfM). 28.

(38) . 3.3.1 (Affine-SIFT) [15]. (approximate nearest neighbors, ANN) [24]. A. kd-Tree. B. B. kd-Tree A. kd-Tree. A. B. B. RANSAC [25] (initial minimal data sets) RANSAC. [26] (Bundle. Adjustment). (Clustering Views for Multi-view Stereo, CMVS). [9]. 29.

(39) . (Patch-based Multi-View Stereo, PMVS). [8]. 3.4 (. GPS. ) EXIF. ). GPS. (. SfM. (Alignment). (Bundle Adjustment) GPS. 3.4.1. (Global Coordinate Systems). (Local-Level Coordinate System). (earth-centered earth-fixed ECEF). (earth-centered inertial; ECI). 30.

(40) . ( (Geocentric Longitude ϕ). 3.9). (Geocentric Latitude λ) (Oblate Ellipsoid) (. 3.9. (Geocentric Longitude). 31. 3.10). (Geocentric Latitude).

(41) . 3.10 ECFC ECEF. Z. (. 3.11). 10. 31. a. b. x. z. xz (Reference Meridian). xy. (Mean Equator) a. Z9 =. b (_ ` Xa ` ) _`. (. 3.1). ; H=. (_Xa). (. 3.2). Z 9 = 2H − H 9. _. 32. (. 3.2). (. 3.1).

(42) . 3.11. §. WGS84(World Geodetic System) GPS <geo_x>= longitude <geo_y>= latitude. §. UTM(Universal Transverse Mercator Projection System). WGS84 UTM 32N. <geo_z>= altitude. <geo_x>= E. 33. <geo_y>= N.

(43) . §. JPEG EXIF width) SfM. (camera sensor. EXIF (. ) EXIF. cdefghij = Hpqrst). : EXIF wt). , ℎt). :. (. Hpqrsuv : EXIF. ) (. kfj(lhij , mhij ) ∗ cdefgkk eeolkk. ). (. ). qqywuu :. (. ). 3.4.2 GPS Geodesy. (. GPS XYZ). GPS GPS GPS. SfM. XYZ. 34. XYZ.

(44) . (1). EXIF (latitude/longitude/altitude. GPS. LLA). XYZ. KD-Tree GPS. (earth-centered earth-fixed ECEF) ECEF. (0,0,0) y. LLA 3×1. x. 90. z. ECEF. ECEF. +z. µ. τ. ℎ. Y}. +. ~} cos Y} cos τ + ℎ cos µ cos τ +z = +2 = ~} cos Y} sin τ + ℎ cos µ sin τ ~} sin Y} + ℎ sin µ +U ~}. (flattening, H). Y} = atan ((1 − H)9 tan á). ~} =. ?9 1+(. 1 − 1)/àâ9 Y} (1 − H)9. 35. R.

(45) . (2). SfM. (3) GPS. Kd-tree. (4). SfM. GPS. SfM (pixel pitch). 7-DoF(degree of freedom) 6}. 36.

(46) . GPS. 6}. GPS. GPS RANSAC. [20]. GPS. 3.4.3. 7-DoF. (Similarity Transform) (Euclidean) "ä. A (. D. 3.3) "ã = /?"ä + ;. /. ? (å (_ (. (. 3.3). ; (_. 7-DoF. (_ ∈ "ã (å. 3.4). 37. (å ∈ "ã. [27].

(47) . é_,) = (_,) − (_. (. 3.4). éå,) = (å,) − (å é_,) éå,) 3.5. é_,). éå,). 33. 9. / = é_,). í ëìî í ëìî. `. èê,ë. (. `. èï,ë. éå,). 3.5). ?. Kabsch. (least squares) 3.6. ; = (_ − /?(å. 3.12. (a). (b). 38. (. 3.6). [23].

(48) . (_. (å "ä. RANSAC[20]. "ä. "ã. "ã. SfM. "ä. SfM "ã. GPS. 34 SfM. GPS. 313- SfM GPS. 3.14 (b). SfM. 3.14 (a). ( SfM. 39. ).

(49) . 3.14 –. [27] (å (1). (2). 35(b) SfM. GPS/INS. (3). [25]. 2 3×4. +ò. j () ∈ "ã. ó),ò = +ò (). 0 = ó),ò ⊗ +ò (). 40. ó),ò.

(50) . ö() = 0 ( =1. ö(. öS ö. (). ö = õΣù S. à ûü. ù. SfM SfM. (. ). (_. WCS (å. 3.15 (b). 3.15 – (a). (b). 41. [27].

(51) . 4.1 4.2. 4.1 (1). (. 1) HP ProDesk 600 G1 SFF Ubuntu 16.04 LTS – 64bit Intel Core i5-4580 CPU @ 3.20 GHz x 4 8 GiB Intel Haswell Desktop 1.0 TB 1–. (2). (. 2) APPLE iPhone 6 Plus iOS 10.3.2 A8. CPU. PowerVR GX6450 5.5. 42.

(52) . 1920 × 1080 GPS v. v. v. v. 2–. 4.2. 4.2.1. ( A (. B. ). (. ). 3–. (Independent variable) (Dependent variable). 43. 4).

(53) . § 14. 44.

(54) . 45.

(55) . § 18. 46.

(56) . § 20. 47.

(57) . 48.

(58) . §. 46. 49.

(59) . 50.

(60) . KeyFrame 14. 15432. 2 mins. 18. 15492. 3 mins 40s. 20. 14692. 5 mins. 46. 31347. 26 mins. Stuffed toy - Melody. Stuffed toy - Big Bear. Summerhouse. Liberty Square 4–. §. 51.

(61) . §. §. §. 52.

(62) . 4.2.2 GPS. §. SfM GPS EXIF ECEF. 53.

(63) . §. SfM GPS EXIF ECEF. 54.

(64) . §. SfM GPS EXIF ECEF. 55.

(65) . SfM. SfM+GPS. SfM. SfM+GPS. 12873. 15432. 2 mins 30s. 2 mins. 13650. 15492. 3 mins 40s. 3 mins 20s. 24327. 14692. 7 mins 10s. 5 mins. 34932. 31347. 50 mins. 26 mins. 5–. 4.2.3 (Keyframe). Sample Analysis- SummerHouse Time (minute). 12 10 8 6 4 2 0 Feature Extraction Incremental & Matching Reconstruction. Bundle Adjustment 10. 20. GPS Coordinate Transformation 30. KeyFrame (piece). 56. Multi-view Calculation.

(66) . Sample Analysis- Liberty Square Time (minute). 20 15 10 5 0 Feature Extraction Incremental & Matching Reconstruction. Bundle Adjustment 10. GPS Coordinate Transformation. 20. Multi-view Calculation. 30. KeyFrame (piece). •. (. 4.2.2. ) 4.2.3. •. 4.2.1. 57.

(67) . •. 4.2.2. GPS. 58.

(68) . SfM. GPS. ASIFT GPS. 5.1. 59.

(69) . A. (SIFT). (Difference of Gaussian; DoG). (Laplacian of Gaussian; LoG) SIFT. LoG SIFT. A.1. A.1. SIFT. 60.

(70) . (1). (Linear smoothing filter). (Gaussian Blur). G. G x, y, σ = . 8 9§• `. Z X(.. G x, y, σ ® x, y, σ. ` ¶2 ` )/9• `. (. ß((, *). a.1). (convolution). a.2. ® x, y, σ = G x, y, σ ∗ ß((, *) ß((, *). σ. (. ∗. a.2) σ. ( (. ). ) (. Lowe(1999). ). (DoG scale space) © x, y, σ. a.3. LoG a.4. © x, y, σ = (G x, y, kσ − ´ (, *, σ ) ∗ ß((, *). 61. (. a.3).

(71) . = ® x, y, kσ − ® (, *, σ. (. a.4). k Mikolajczyk(2004). LoG (Gradient). Harris. Hessian. Lindeberg(1994) ¨ 9 ∇9 ´. DoG. ÆØ Æ∞. = ¨ 9 ∇9 ´ . ¨ 9 ∇9 ´ = . ÆØ Æ∞. ≈. (. Ø(.,2,≤•) ≤•X •. a.5). (. a.6). a.7. ´ (, *, ≥¨ − ´ (, *, ¨ ≈ (≥ − 1)¨ 9 ∇9 ´ ß. ¨. (. a.7). ¨. (down sampling) (Scale-invariant). ≥. î. 2¥. s. s. Lowe(2004). 62. 3~5. ¨ = 1.6 s = 3.

(72) . A.2. A.2. [4]. 3 × 3 × 3 A.3 8. 18 (. 26. (keypoint). 63. X 9 × 2).

(73) . A.3. [4]. (2). (DoG. ). ( (. a.3). © x, y, σ. A.4). ( a.8). © " = © + . µã ∂ µM. " = ((, *, ¨)S. µã ∂. 9. µM `. (. " (, *, ¨ = −. 8. " + "S. (. a.9). µ ` ã ∑î µã µ ` M ` µM. 64. ". (. a.9). a.8).

(74) . A.4 Harris(1998) Hessian 2×2 Hessian. (. a.10). H =. ©.. ©.2. ©.2 ©22. H α. (. a.10). ©. H. β. α. β. γ. 6º Ω = ©.. + ©.2 = - + æ ©Z; Ω = ©.. ©22 − ©.2 Sø ¿ ` ã¡û ¿. =. (¬¶√)` ¬√. =. (ƒ√¶√ ` ) ¬√. 65. =. 9. = -æ. (ƒ¶8)` ƒ. (. (. a.11. a.11). (. a.12). 12).

(75) . (3). ®. (. K. a.13). ≈ K (, * =. (® ( + 1, * − ®(( − 1, *))9 + (® (, * + 1 − ® (, * − 1 )9. ≈((, *) = tanX8 ((® (, * + 1 − ®((, * − 1))/(® ( + 1, * − ®(( − 1, *))). 0~360. 10. 80%. A.5. SIFT. 66. (. a.13). (. A.5).

(76) . (4). SIFT. A.6. (. ). 4×4 4×4×4 = 128. 8. A.6. 8. SIFT. 67. 45 SIFT.

(77) . B. (Translation Invariant) Invariant). (Affine-SIFT). Harris. [28]. Harris Laplace Hessian Laplace (Affine Invariant). (Scale. DoG (Difference of Gaussian)[29] MSER(Maximally Stable. Extremal Regions)[30]. ASIFT (1) (2) (3). SIFT. (4). SIFT. (i.e.. ) (Transition tilt). 68.

(78) . § B.1. B.1. [15]. ó = T8 ´8 öó0 ( b.1) ´8 ö. (Gaussian kernel) T8. (CCD). (projective planar transform). ó. (Affine Simplification) B.2. 69. (Sampling).

(79) . b.1. b.2. ó = ´8 ö«0 ( b.2). B.2. [15]. (Affine Transform). X-Y r. ». q y Z. ( (. b.4). H. b.3) (. 70. b. 3. b.5).

(80) . B.3 B.3. [15]. b.1. (. ö = ΩÀ ?8 (Ã)6û ?9 (f). l>0. ). 6û (;>1). (. b.6). l. Ã f q. 8. (Latitude) q = arccos( ). (Longitude). û. ; >1 « qÎ 0°, 90°. 4 ó0. l. Ã. 71. (. ).

(81) . §. (Transition Tilts). ó x, y. ó8. ó8 x, y = u ö (, * t. ó9. ó9 (, * = ó(—((, *)). 2.18. —öX8 = ΩÀ ?8 (Ã)6“ ?9 (”) ( b.7). B.4. (1). [15]. t ó8 , ó9 = t ó9 , ó8 f t ó8 , ó9 = τ ;, ; ‘ , ” − ” ‘. (2) (3). û÷. ; ‘ = max ; ‘ , ;. û. 72. £ t £ ; ‘ ;.

(82) . ” = ” ‘. B.5 t ó8 , ó9 =. B.5. ó9. t ó8 , ó9 = ; ‘ ;. û. (Longitude). ó8. ). û÷. B.5 §. (. [15] (Latitude). ASIFT. (f). (q). (Absolute tilts) ; = 1, r, r9 , … , rÿ â³5. t. 1~32. a= 2 ∆; =. 73. û›ﬁî û›. = 2. r > 1.

(83) . ﬂ. B.1. ∆ϕ = ”≤¶8 − ”≤ = ∆” = 72°/;. a. ;. 0, , … , ≥»/; û. » = 72°. ≥. ≥»/;< 180° B.6. B.6. [15]. Y. Z ASIFT ASIFT. 74.

(84) . ASIFT (High-resolution) (Low-resolution). ·×·. (1). ó T„ ´„ ‚. ‚. ó‘ = T„ ´„ ó. W×W. ´„. (öâ;à −. rspr/àâ‰ ´ró//àrâ yà/q~Z;Z Hàs;Z~). T„. W×W. (2) u‘. v‘. ASIFT. (3) u. B.7. SIFT. 3x3=9. 19 SIFT. v. 51. 75. ‚‘ =.

(85) . B.7. §. [15]. ASIFT SIFT. ;u)ÿ , ;u_. = [1, 4 2]. 76. ASIFT.

(86) . ”u)ÿ , ”u_. = [0°, 180°] ∆; = 2. ℒÁ = 1. ;=1 8Ë0 È9/Á. 2 2 2 2 4 4 2 =6 1. = 2.5t. ∆ϕ = 72°/t 8. ;. û. ;. 1 + ℒÁ − 1 180/72 W×W W×W. 3x3. ASIFT SIFT. SIFT. §. 1.5. ASIFT. 2.25. ASIFT. ASIFT. 1. 2.. (Latitude). (Longitude) (Rotation) (f). (Translation). (Scale). (q). ∆; = 2 ∆” = 72°/;. 77.

(87) . SIFT. ASIFT ASIFT. SIFT. SIFT. 78.

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